Newton’s laws and consideration of units are used to present and discuss the mass on a spring as an example of a harmonic oscillator, a mechanical oscillator with a sinusoidal time dependence. Both the transient solution, where the oscillator is started away from equilibrium and left on its own, and the driven solutions, where a sinusoidal driving force is applied, are presented. The quality factor, Q, is introduced, which characterizes the relative amount of damping forces present, such as those of friction or air drag. The quality factor is related to the number of oscillations that are made when left on its own and to the excitation bandwidth, the range of frequencies over which resonance is observed. Musically relevant examples include the ocarina, tuning fork, some speaker enclosures, and the phenomenon of sympathetic resonance.
Review the options below to login to check your access.
Log in with your Cambridge Higher Education account to check access.
If you believe you should have access to this content, please contact your institutional librarian or consult our FAQ page for further information about accessing our content.